Custom user registration

I want to Implement custom user registration process in my wordpress theme. Can anyone please explain me the complete process for user registration.

Note:
I don’t want to use default register action of wordpress. I know that we can register users through url:

http://site-name.com/wp-login.php?action=register

I want to design my own user registration form. So kindly do not suggest any plugin or gravity forms or any other third party software/plugin.